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Manipal Entrance Test 2015 Math Paper
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© examsnet.com
Question : 2
Total: 70
(
a
.
^
i
)
(
a
×
^
i
)
+
(
a
.
^
j
)
(
a
×
^
j
)
+
(
a
.
^
k
)
(
a
×
^
k
)
isequal to
3a
a
0
None of these
Validate
Solution:
Let
a
=
a
1
^
i
+
a
2
^
j
+
a
3
^
k
Then,
a
.
^
i
=
a
1
,
a
.
^
j
=
a
2
,
a
.
^
k
=
a
3
a
×
^
i
=
−
a
2
k
+
a
3
^
j
,
a
×
j
=
a
1
^
k
−
a
3
^
i
and
a
×
^
k
=
−
a
1
^
j
+
a
2
^
i
∴
(
a
.
^
i
)
(
a
×
^
i
)
+
(
a
.
^
j
)
(
a
×
^
j
)
+
(
a
.
^
k
)
(
a
×
^
k
)
=
a
1
(
−
a
2
^
k
+
a
3
^
j
)
+
a
2
(
a
1
^
k
−
a
3
^
i
)
+
a
3
(
−
a
1
^
j
+
a
2
^
i
)
=
0
© examsnet.com
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